CN101887238A - Specific repetitive controller and control method - Google Patents

Abstract

The invention discloses a specific repetitive controller and a control method. The controller comprises a repetitive control gain module, a negative feedforward gain module, a position feedforward module, two addition rings and three time delay modules. In the method, a main path, a positive feedforward path, a negative feedforward path and a positive feedback path are combined to realize error-free (nk+/-m) harmonic tracking or eliminating, wherein the parameters of the positive and negative feedforward gain modules are determined according to the times of the harmonics to be traced or eliminated, and the error elimination speed is regulated by the repetitive control gain module. The controller and the method has the advantages of achieving a high error elimination speed, using fewer storage units for realizing digitalization and providing a general repetitive controller expression mode. For improving the stability and anti-interference performance of the system, the invention also provides an improved (nk+/-m) harmonic repetitive controller which has a low pass filter and a phase advancer to meet requirements for practical use.

Description

A kind of specific repetitive controller and control method

Technical field

The present invention proposes a kind of specific repetitive controller and control method, be used for that (the error free tracking of the rd harmonic signal of nk ± m) or eliminate fully belongs to the repetitive controller field of Industry Control.

Background technology

For many years, the tracking of cyclical signal and Disturbance Rejection compensation problem are the problems that numerous researchists pay close attention to always, and based on internal model principle to repeat control be exactly a kind of highly effective control device.It is T that general repetitive controller adopts delay time T _oThe positive feedback form of delay link

Constructing the primitive period is T _oThe internal mold of periodic signal, and with in it embedding control loop, thereby can implement static indifference tracking Control or disturbance is eliminated to this kind cyclical signal (comprising sinusoidal fundamental wave and each harmonic thereof), because such repetitive controller is by being the time delay that is input to output primitive period T _o, its response speed is relatively slow, and repetitive controller is many with digital form z in the middle of actual ^-N/ (1-z ^-N) (N=T wherein _o/ T _sBe integer, T _sBe the sampling time) realize the internal mold of this cyclical signal, its shared internal storage location number is at least N.Yet in some practical applications, the harmonic wave that needs to follow the tracks of or eliminate is confined to some specific frequency, for example the three phase rectifier load concentrates on 6k ± 1 (k==1 for the harmonic pollution overwhelming majority that power-supply system caused, 2, ...) the subfrequency place, and the single-phase rectifier load give the harmonic pollution overwhelming majority that power-supply system caused concentrate on 4k ± 1 (k==1,2 ...) and subfrequency (being odd harmonic frequencies) locates.If (the periodic disturbance phenomenon very slowly that disappears can appear in the subharmonic of nk ± m), often can't satisfy the requirement of real system to control performance to adopt general repetitive controller to eliminate this class.If can propose new repetitive controller only compensates at these frequencies, by transforming the internal mold of signal in the controller, its control lag time is shortened, and the speed of disturbance is eliminated by raising system greatly, and significantly reduces the required storage space that takies of its Digital Implementation.Therefore be necessary still that the multiple control technology of counterweight does further research.

Summary of the invention

Technical matters: the objective of the invention is to propose a kind of specific repetitive controller and control method, this repetitive controller is only at (nk ± m) rd harmonic signal is followed the tracks of fully or eliminated, it is far away from general repetitive controller that the speed of its tracking or harmonic carcellation signal is wanted, and the shared storage space of its Digital Implementation still less, and its cost performance promotes greatly.

Technical scheme:

The present invention adopts following technical scheme for achieving the above object:

A kind of specific repetitive controller of the present invention, comprise repetition ride gain module, negative feedforward gain module, positive feedforward gain module, the addition ring, two time delay modules that the subtraction ring is identical with three, the output terminal that wherein repeats the ride gain module connects the input end of addition ring and negative feedforward gain module respectively, connect the input end of the second time delay module and positive feedforward gain module behind the output terminal serial connection very first time Postponement module of addition ring respectively, the output terminal of negative feedforward gain module is connected in series the negative input end that connects the second subtraction ring after the 3rd time delay module, the negative input end of the output termination first subtraction ring of the second time delay module, the positive input terminal of the output termination first subtraction ring of positive feedforward gain module, the positive input terminal of the output termination second subtraction ring of the first subtraction ring, the input end of the output termination addition ring of the second subtraction ring.

Preferably, the output terminal of described three identical time delay modules is connected in series low-pass filter respectively, the output terminal serial connection phase lead compensation module of the described second subtraction ring.

Preferably, described time delay module is an analog or digital time delay module.

A kind of control method of specific repetitive controller is as follows:

Repeat the ride gain module: the input quantity of repetitive controller is obtained repetition ride gain module output quantity through repeating ride gain, realize regulating the speed that specific subharmonic was followed the tracks of or eliminated to described repetitive controller by regulating the repetition ride gain;

Negative feedforward gain module: will repeat ride gain module output quantity and obtain negative feedforward gain module output quantity through negative feedforward gain, parameter is determined by the harmonic frequency number of times that will follow the tracks of or eliminate in the negative feedforward gain;

The addition ring: the output quantity addition that will repeat ride gain module output quantity and repetitive controller obtains addition ring output quantity;

Very first time Postponement module: addition ring output quantity is postponed output;

The second time delay module: the addition ring output quantity that very first time Postponement module is postponed output postpones output again;

The 3rd time delay module: will bear feedforward gain module output quantity and postpone output;

Positive feedforward gain module: the addition ring output quantity that very first time Postponement module is postponed output obtains positive feedforward gain module output quantity through positive feedforward gain, parameter is determined by the harmonic frequency number of times that will follow the tracks of or eliminate in the positive feedforward gain, cooperates with negative feedforward gain module to realize following the tracks of or eliminating specific subharmonic;

The first subtraction ring: the output quantity and the positive feedforward gain module output quantity of the second time delay module are subtracted each other back output;

The second subtraction ring: the first subtraction ring output quantity and the 3rd time delay module are subtracted each other the output quantity that obtains repetitive controller.

Preferably, described time delay module is an analog or digital time delay module, and then described repetitive controller transport function is as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\·\frac{\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{s\frac{T_o}{n}}+1}$

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\·\frac{\cos \left(\frac{2\mathrm{\π}}{n}m\right)\·z^{\frac{N}{n}}-1}{z^{2\·\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)\·z^{\frac{N}{n}}+1}$

Wherein c () is the output quantity of repetitive controller, and e () is the input quantity of repetitive controller that is the departure amount of control system, k _rFor repeating ride gain, z is the variable of the z conversion of discrete-time system, and s is Laplce (Laplace) variable of continuous time system, N=T _o/ T _sBe integer, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe first-harmonic angular frequency, T _sBe the sampling period, n, k and m are not less than zero integer and n ≠ 0, n＞m.

Preferably, described time delay module is the simulated time Postponement module, then eliminate (nk ± m) the repetitive controller transport function of subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\·\frac{\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)e^{s\frac{T_o}{n}}+1}=k_r\·\frac{\cos \left(\frac{2\mathrm{\π}}{n}m\right)-e^{s\frac{T_o}{n}}}{e^{s\frac{T_o}{n}}+e^{-s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\π}}{n}m\right)}$

$=\frac{1}{2}{k}_r\·\frac{\cos \left(\frac{2\mathrm{\π}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{\cosh \left(s\frac{T_o}{n}\right)-\cos \left(\frac{2\mathrm{\π}}{n}m\right)}$

$=\frac{1}{2}{k}_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{2s{\mathrm{in}}^2\left(\frac{2\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="1"\; label="n\; m"\; filenames="HSA00000180360000013.png"\; state="\{\{state\}\}">n</figure-callout>}}m\frac{1}{2}\right)\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Following formula requires m ≠ 0; When m=0, eliminate (nk ± m) the repetitive controller transport function of subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}{|}_{m=0}=k_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2e^{s\frac{T_o}{n}}+1}$

${=k}_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{{(e^{s\frac{T_o}{n}}-1)}^2}=k_r\&CenterDot;\frac{1}{e^{s\frac{T_o}{n}}-1}$

$=k_r\&CenterDot;\frac{1}{\frac{s{T}_o}{n}\&CenterDot;e^{\frac{{\mathrm{sT}}_o}{2n}}\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Comprehensive above-mentioned two formulas are the (ω of nk ± m) so the specific subharmonic repetitive controller that the present invention proposes comprises frequency _oLimit, therefore also claim (the subharmonic repetitive controller of nk ± m).

Preferably, the output terminal of described three identical time delay modules is connected in series low-pass filter Q () respectively and carries out filtering, the output terminal serial connection phase lead compensation modules A () of the described second subtraction ring is carried out phase lead compensation, and then its repetitive controller transport function is as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)-Q^2\left(s\right)}{e^{s\frac{2T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)+Q^2\left(s\right)}\&CenterDot;A\left(s\right)$

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)-Q^2\left(z\right)}{z^{2\&CenterDot;\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)+Q^2\left(z\right)}\&CenterDot;A\left(z\right)$

Beneficial effect:

It is 1, proposed by the invention that (the subharmonic repetitive controller of nk ± m) is specially at (rd harmonic signal of nk ± m) carries out error free tracking or disturbance is eliminated, can customize different n and the numerical value of m according to the actual demand of harmonic carcellation disturbing signal or tracking reference signal.As at eliminating (6k ± 1) subharmonic in the three-phase inversion and following the tracks of the needs of first-harmonic reference signal, only need make n=6 and m=1 get final product; To eliminating odd harmonic in the single-phase inversion and following the tracks of the needs of first-harmonic reference signal, only need make n=4 and m=1 get final product.Compare with general repetitive controller, its speed of eliminating disturbance improves greatly.

2, (nk ± m) number of the required storage unit of Digital Implementation of subharmonic repetitive controller also is significantly less than general repetition of figures controller.

3, (nk ± m) the subharmonic repetitive controller has provided a kind of universal expression formula of repetitive controller, unified multiple repetitive controller, " the Zero-phase Odd-harmonic Repetitive Controller fora Single-phase PWM Inverter " that is shown as document Keliang Zhou etc., IEEE Trans.on Power Electronics, Vol.21, No.1, pp.193-201, applied odd harmonic repetitive controller is the present invention's (special case of subharmonic repetitive controller when n=4 and m=1 of nk ± m) in 2,006 one literary compositions; And general repetitive controller can (nk ± m) the subharmonic repetitive controller makes n=1 and m=0 obtain by the present invention.

4, (ratio that the subharmonic repetitive controller of nk ± m) is used for eliminating nk+m and these two kinds of frequencies of nk-m only needs a kind of time delay link to construct the disturbing signal internal mold during not for the disturbance of integral multiple relation, has therefore simplified the design of time delay link in the repetitive controller.

Description of drawings

Fig. 1 is that the present invention proposes (the subharmonic repetitive controller of nk ± m).

Fig. 2 is the Digital Implementation form of Fig. 1, is (the subharmonic repetition of figures controller of nk ± m).

Fig. 3 is improved (the subharmonic repetitive controller of nk ± m) that adds low-pass filtering link and phase lead compensation link on Fig. 1 basis.

Fig. 4 is the Digital Implementation form of Fig. 3, is improved (the subharmonic repetition of figures controller of nk ± m).

Fig. 5 is improved (the subharmonic repetition of figures controller of nk ± m) the control system structured flowchart of general feedback controller that superposes.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

Proposed by the invention (the subharmonic repetitive controller structured flowchart of nk ± m) as shown in Figure 1, its transport function is:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{s\frac{{2T}_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}$

Wherein c (s) is the output quantity of repetitive controller, and e (s) is the input quantity of repetitive controller that is the departure amount of control system, k _rFor repeating ride gain, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe the first-harmonic angular frequency, n, k and m are not less than zero integer and n ≠ 0, n＞m.By regulating gain coefficient k _rNumerical value, can change the speed of convergence of system, k _rBig more, system's convergent speed is fast more, but k _rCross conference and cause system to exceed range of stability, so k _rCan only improve the speed of convergence of system within the specific limits.Three delay links among Fig. 1 are identical, and its delay time T all equals primitive period T _oN/one, long delay time path is made up of two above-mentioned delay links, so its total delay time is (2T _o/ n)＜＜T _o, therefore repeating ride gain k _rUnder the identical situation, the response speed of this repetitive controller is more faster than general repetitive controller, and this is (the big advantage of subharmonic repetitive controller of nk ± m).

Because the transport function of the repetitive controller that the present invention is shown in Figure 1 can be rewritten as follows:

$G_{\mathrm{rc}}\left(s\right)=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)-e^{s\frac{T_o}{n}}}{e^{s\frac{T_o}{n}}+e^{-s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=\frac{1}{2}{k}_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{\cosh \left(s\frac{T_o}{n}\right)-\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=\frac{1}{2}{k}_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{2s{\mathrm{in}}^2\left(\frac{2\mathrm{\&pi;}}{\mathrm{<figure-callout\; id="1"\; label="n\; m"\; filenames="HSA00000180360000013.png"\; state="\{\{state\}\}">n</figure-callout>}}m\frac{1}{2}\right)\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Following formula requires m ≠ 0; When m=0, eliminate (nk ± m) the repetitive controller transport function of subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}{|}_{m=0}=k_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2e^{s\frac{T_o}{n}}+1}$

${=k}_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{{(e^{s\frac{T_o}{n}}-1)}^2}=k_r\&CenterDot;\frac{1}{e^{s\frac{T_o}{n}}-1}$

$=k_r\&CenterDot;\frac{1}{\frac{s{T}_o}{n}\&CenterDot;e^{\frac{{\mathrm{sT}}_o}{2n}}\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Comprehensive above-mentioned two formulas, the limit that therefore can get repetitive controller shown in Figure 1 is the (ω of nk ± m) in frequency _oThe place, promptly pole frequency is m ω _o, (the ω of n ± m) _o, (the ω of 2n ± m) _o..., (the ω of in ± m) _o... (i=1 wherein, 2,3...).Because this repetitive controller is the (ω of nk ± m) in frequency _oThe gain at place be infinitely great, therefore can thoroughly eliminate frequency among the departure e (s) and be (the ω of nk ± m) _oHarmonic component, thereby realize (nk ± m) elimination fully or the error free tracking of subharmonic disturbance is so with this repetitive controller, i.e. the specific subharmonic repetitive controller of the present invention proposition is called (the subharmonic repetitive controller of nk ± m).In the middle of the practical application, can be at the demand of different occasions, give m and n with different numerical value, can realize specific (nk ± m) the error free tracking or the Disturbance Rejection of subharmonic.For example for the situation of three-phase inverter band three phase rectifier load, because its harmonic wave mainly concentrates on (6k ± 1) inferior (i.e. 5,7,11,13 grades) harmonics frequency component place, and often need follow the tracks of the first-harmonic reference signal, so only need make n=6 and m=1, just can realize to the error free tracking of first-harmonic reference signal with to the elimination fully of (6k ± 1) subharmonic; Situation for single-phase inverter band single-phase rectifier load, because its harmonic wave mainly concentrates on (4k ± 1) inferior (promptly 3,5,7,9 etc. odd) frequency component place, and often need follow the tracks of the first-harmonic reference signal, so only need make n=4 and m=1, just can realize to the error free tracking of first-harmonic reference signal with to the elimination fully of odd harmonic.

Repetitive controller is many in the middle of actual is realized and is used with digital form.The pairing Digital Implementation of repetitive controller shown in Figure 1 as shown in Figure 2, its transport function is:

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}-1}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000180360000011.png,HSA00000180360000012.png"\; state="\{\{state\}\}">z</figure-callout>}}^{2\&CenterDot;\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}+1}$

Wherein c (z) is the output quantity of repetitive controller, and e (z) is the input quantity of repetitive controller that is the departure amount of control system, k _rFor repeating ride gain, N=T _o/ T _sBe integer, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe first-harmonic angular frequency, T _sBe the sampling period, n, k and m are not less than zero integer and n ≠ 0, n＞m.Three time delay links among Fig. 2 are identical, the internal storage location number that takies all is N/n, therefore its total internal storage location number is (3N/n), therefore (storage space that the subharmonic repetition of figures controller of nk ± m) takies is wanted much less than general repetition of figures controller, and this is (another big advantage of subharmonic repetitive controller of nk ± m).

In actual applications, for improving the stability and the antijamming capability of control system, usually need among Fig. 1 or Fig. 2 (nk ± m) the subharmonic repetitive controller is improved, improved method is to add low-pass filter link Q (s) or Q (z) and phase lead compensation link A (s) or A (z) in repetitive controller, as shown in Figure 3 and Figure 4, wherein Fig. 4 is the Digital Implementation form of Fig. 3.Shown in Figure 3 improved (nk ± m) transport function of subharmonic repetitive controller can be write as following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)-Q^2\left(s\right)}{e^{s\frac{2T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)+Q^2\left(s\right)}\&CenterDot;A\left(s\right)$

Shown in Figure 4 improved (nk ± m) transport function of subharmonic repetition of figures controller can be write as following form:

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)-Q^2\left(z\right)}{{\mathrm{<figure-callout\; id="2"\; label="z"\; filenames="HSA00000180360000011.png,HSA00000180360000012.png"\; state="\{\{state\}\}">z</figure-callout>}}^{2\&CenterDot;\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)+Q^2\left(z\right)}\&CenterDot;A\left(z\right)$

It is of the present invention that (the subharmonic repetitive controller of nk ± m) can be to insert or cascade system joins the (order harmonic components of nk ± m) that is used in the general feedback control system to eliminate in the middle of the departure.Below with will (it be example that the subharmonic repetition of figures controller of nk ± m) joins in the general feedback system with inserted mode, introduces (the embodiment of subharmonic repetitive controller of nk ± m) proposed by the invention.Shown in Figure 5 is that (nk ± m) subharmonic repetition of figures controller joins the structured flowchart in the general feedback control system, wherein G with improved _Rc(z) be improved (the subharmonic repetition of figures controller of nk ± m), G _c(z) be conventional feedback controller, G _s(z) be controlling object, y _d(z) for reference of system input and be generally the first-harmonic reference signal, y (z) be the actual output of system, and e (z) is reference and the error while of actual signal also is repetitive controller G _Rc(z) input signal, c (z) is repetitive controller G _Rc(z) output signal simultaneously also after error signal e (z) addition as conventional feedback controller G _c(z) input, u (z) is conventional feedback controller G _c(z) output signal also is controlling object G simultaneously _s(z) input signal, d (z) are the disturbance input signal of system, it and controlling object G _s(z) output signal addition forms real output signal y (z).

Claims (7)

1. specific repetitive controller, it is characterized in that comprising repetition ride gain module, negative feedforward gain module, positive feedforward gain module, the addition ring, two time delay modules that the subtraction ring is identical with three, the output terminal that wherein repeats the ride gain module connects the input end of addition ring and negative feedforward gain module respectively, connect the input end of the second time delay module and positive feedforward gain module behind the output terminal serial connection very first time Postponement module of addition ring respectively, the output terminal of negative feedforward gain module is connected in series the negative input end that connects the second subtraction ring after the 3rd time delay module, the negative input end of the output termination first subtraction ring of the second time delay module, the positive input terminal of the output termination first subtraction ring of positive feedforward gain module, the positive input terminal of the output termination second subtraction ring of the first subtraction ring, the input end of the output termination addition ring of the second subtraction ring.

2. a kind of specific repetitive controller according to claim 1 is characterized in that the output terminal of described three identical time delay modules is connected in series low-pass filter respectively, the output terminal serial connection phase lead compensation module of the described second subtraction ring.

3. a kind of specific repetitive controller according to claim 1 and 2 is characterized in that described time delay module is an analog or digital time delay module.

4. control method based on the described a kind of specific repetitive controller of claim 1 is characterized in that described method is as follows:

Repeat the ride gain module: the input quantity of repetitive controller is obtained repetition ride gain module output quantity through repeating ride gain, realize regulating the speed that specific subharmonic was followed the tracks of or eliminated to described repetitive controller by regulating the repetition ride gain;

Negative feedforward gain module: will repeat ride gain module output quantity and obtain negative feedforward gain module output quantity through negative feedforward gain, parameter is determined by the harmonic frequency number of times that will follow the tracks of or eliminate in the negative feedforward gain;

The addition ring: the output quantity addition that will repeat ride gain module output quantity and repetitive controller obtains addition ring output quantity;

Very first time Postponement module: addition ring output quantity is postponed output;

The second time delay module: the addition ring output quantity that very first time Postponement module is postponed output postpones output again;

The 3rd time delay module: will bear feedforward gain module output quantity and postpone output;

Positive feedforward gain module: the addition ring output quantity that very first time Postponement module is postponed output obtains positive feedforward gain module output quantity through positive feedforward gain, parameter is determined by the harmonic frequency number of times that will follow the tracks of or eliminate in the positive feedforward gain, cooperates with negative feedforward gain module to realize following the tracks of or eliminating specific subharmonic;

The first subtraction ring: the output quantity of the positive feedforward gain module output quantity and the second time delay module is subtracted each other back output;

The second subtraction ring: the first subtraction ring output quantity and the 3rd time delay module are subtracted each other the output quantity that obtains repetitive controller.

5. the control method of a kind of specific repetitive controller according to claim 4 is characterized in that described time delay module is an analog or digital time delay module, and then described repetitive controller transport function is as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}$

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}-1}{z^{2\&CenterDot;\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}+1}$

Wherein c () is the output quantity of repetitive controller, and e () is the input quantity of repetitive controller that is the departure amount of control system, k _rFor repeating ride gain, z is the variable of the z conversion of discrete-time system, and s is Laplce (Laplace) variable of continuous time system, N=T _o/ T _sBe integer, T _oBe the primitive period, T _o=2 π/ω _o=1/f _o, f _oBe fundamental frequency, ω _oBe first-harmonic angular frequency, T _sBe the sampling period, n, k and m are not less than zero integer and n ≠ 0, n＞m.

6. the control method of a kind of specific repetitive controller according to claim 5 is characterized in that adopting the simulated time Postponement module, eliminate (nk ± m) the repetitive controller transport function of subharmonic can change into following form:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)-e^{s\frac{T_o}{n}}}{e^{s\frac{T_o}{n}}+e^{-s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=\frac{1}{2}{k}_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{\cosh \left(s\frac{T_o}{n}\right)-\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)}$

$=\frac{1}{2}{k}_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right){-e}^{-s\frac{T_o}{n}}}{2s{\mathrm{in}}^2\left(\frac{2\mathrm{\&pi;}}{n}m\frac{1}{2}\right)\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

Following formula requires m ≠ 0; When m=0, eliminate (nk ± m) the repetitive controller transport function of subharmonic is as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}+1}{|}_{m=0}=k_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{e^{2s\frac{T_o}{n}}-2e^{s\frac{T_o}{n}}+1}$

${=k}_r\&CenterDot;\frac{e^{s\frac{T_o}{n}}-1}{{(e^{s\frac{T_o}{n}}-1)}^2}=k_r\&CenterDot;\frac{1}{e^{s\frac{T_o}{n}}-1}$

$=k_r\&CenterDot;\frac{1}{\frac{s{T}_o}{n}\&CenterDot;e^{\frac{{\mathrm{sT}}_o}{2n}}\&CenterDot;\underset{k=-\&infin;}{\overset{\&infin;}{\mathrm{\&Pi;}}}[1+\frac{s^2}{{(\mathrm{nk}+m)}^2{\mathrm{\&omega;}}_o^2}]}$

7. the control method of a kind of specific repetitive controller according to claim 5, the output terminal that it is characterized in that described three identical time delay modules is connected in series low-pass filter Q () respectively and carries out filtering, the output terminal serial connection phase lead compensation modules A () of the described second subtraction ring is carried out phase lead compensation, and then its repetitive controller transport function is as follows:

$G_{\mathrm{rc}}\left(s\right)=\frac{c\left(s\right)}{e\left(s\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)-Q^2\left(s\right)}{e^{s\frac{2T_o}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)e^{s\frac{T_o}{n}}\&CenterDot;Q\left(s\right)+Q^2\left(s\right)}\&CenterDot;A\left(s\right)$

Or

$G_{\mathrm{rc}}\left(z\right)=\frac{c\left(z\right)}{e\left(z\right)}=k_r\&CenterDot;\frac{\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)-Q^2\left(z\right)}{z^{2\&CenterDot;\frac{N}{n}}-2\cos \left(\frac{2\mathrm{\&pi;}}{n}m\right)\&CenterDot;z^{\frac{N}{n}}\&CenterDot;Q\left(z\right)+Q^2\left(z\right)}\&CenterDot;A\left(z\right).$

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